Question

Multiple Choice Which of the following is the measure of \(\tan ^{-1}(-\sqrt{3})\) in degrees? \(\begin{array}{llll}{\text { (A) }-60^{\circ}} & {\text { (B) }-30^{\circ}} & {\text { (C) } 30^{\circ}} & {\text { (D) } 60^{\circ}} & {\text { (E) } 120^{\circ}}\end{array}\)

Short answer

-60 degrees

Step-by-step solution

Identify the value of the inverse tangent

The value we're interested in is \(\tan^{-1}(-\sqrt{3})\). This refers to the angle whose tangent is -√3.

Recall tangent values

Remember the tangent values for common angles. The tangent of 60 degrees is √3, and the tangent of -60 degrees is -√3.

Choose the correct answer

The angle whose tangent is -√3 is -60 degrees. Therefore, \(\tan^{-1}(-\sqrt{3})\) is -60 degrees.